Advertisement

Continuum Mechanics and Thermodynamics

, Volume 26, Issue 2, pp 221–245 | Cite as

Description of liquid–gas phase transition in the frame of continuum mechanics

  • Elena N. Vilchevskaya
  • Elena A. Ivanova
  • Holm Altenbach
Original Article

Abstract

A new method of describing the liquid–gas phase transition is presented. It is assumed that the phase transition is characterized by a significant change of the particle density distribution as a result of energy supply at the boiling point that leads to structural changes but not to heating. Structural changes are described by an additional state characteristics of the system—the distribution density of the particles which is presented by an independent balance equation. The mathematical treatment is based on a special form of the internal energy and a source term in the particle balance equation. The presented method allows to model continua which have different specific heat capacities in liquid and in gas state.

Keywords

Liquid–gas phase transition Cluster Chemical potential Source term 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alekhin, A.D., Y.L.O., Rudnikov, E.G.: On the entropy principle of phase transition models with a conserved order parameter. Russian J. Phys. Chem. A Focus Chem. 85 (4), 537–541 (2011)Google Scholar
  2. 2.
    Abeyaratne R., Bhattacharya K., Knowles J.K.: Strain-energy functions with multiple local minima: modeling phase transformations using finite thermoelasticity. In: Fu, Y., Ogden, R.W. (eds.) Nonlinear Elasticity: Theory and Application, pp. 433–490. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
  3. 3.
    Abeyaratne R., Knowles J.K.: Evolution of Phase Transitions. A Continuum Theory. Cambridge University Press, Cambridge (2006)CrossRefGoogle Scholar
  4. 4.
    Alt W.H., Pawlow I.: On the entropy principle of phase transition models with a conserved order parameter. Adv. Math. Sci. Appl. 6, 291–376 (1966)MathSciNetGoogle Scholar
  5. 5.
    Altenbach H., Naumenko K., Zhilin P.: A micro-polar theory for binary media with application to phase-transitional flow of fiber suspensions. Continuum Mech. Thermodyn. 15(6), 539–570 (2003)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Anders D., Weinberg K.: Thermophoresis in binary blends. Mech. Mater. 47, 33–35 (2012)CrossRefGoogle Scholar
  7. 7.
    Baniasadi M., Ghader S., Hashemipour H.: Modifying gma equation of state for description of (p, ρ, t) relation of gas and liquids over an extended pressure range. Korean J. Chem. Eng. 28(3), 939–948 (2011)CrossRefGoogle Scholar
  8. 8.
    Becker R.M.: Theorie der Wärme, 3rd edn. Heidelberger Taschenbücher. Springer, Berlin (1985)Google Scholar
  9. 9.
    Berberan-Santos M.N., Bodunov E.N., Poglian L.: On the entropy principle of phase transition models with a conserved order parameter. J. Math. Chem. 43(4), 1437–1457 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Bonasera A., Di Toro M.: Liquid–gas phase transition and compressibility of nuclear matter. Lettere Al Nuovo Cimento 44(3), 172–176 (1985)CrossRefGoogle Scholar
  11. 11.
    Bowen, R.: Theory of Mixtures. In: Eringen, A.C. (ed.) Continuum Physics, vol. III, pp. 1–127. Academic Press, New York (1976)Google Scholar
  12. 12.
    Cahn J.W.: On spinodal decomposition. Acta Met 9, 795–801 (1961)CrossRefGoogle Scholar
  13. 13.
    Cahn J.W., Hilliard J.: Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258–267 (1958)ADSCrossRefGoogle Scholar
  14. 14.
    de Donde T.: Thermodynamic Theory of Affinity: A Book of Principles. Oxford University Press, Oxford (1936)Google Scholar
  15. 15.
    Fisher, F., Dial, O.E., Jr.: Equation of state of pure water and sea water. Tech. rep., Marine Physical Laboratory of the Scripps Institution of Oceanography, San Diego (1975)Google Scholar
  16. 16.
    Fosdick R.L., Zhang Y.: Coexistent phase mixtures in the antiplane shear of an elastic tube. ZAMP 45, 202–244 (1994)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Freidin A.B., Vilchevskaya E.N.: Multiple development of new phase inclusions in elastic solids. Int. J. Eng. Sci. 47, 240–260 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Gibbs J.W.: On the equilibrium of heterogeneous substances. Trans. Conn. Acad. Sci. III, 108–248 (1875)Google Scholar
  19. 19.
    Ginzburg V.L., Landau L.D.: On the theory of superconductivity. J. Exptl. Theoret. Phys. (U.S.S.R.) 20, 1064 (1950)Google Scholar
  20. 20.
    Green A.E., Naghdi P.M.: A theory of mixtures. Arch. Rat. Mech. Anal. 24(4), 243–263 (1967)CrossRefMathSciNetGoogle Scholar
  21. 21.
    Grigoriev, I.S., Meilikhov, E.Z. (eds.): Handbook of Physical Quantities. CRC Press, Roca Baton (1997)Google Scholar
  22. 22.
    Grmela M.: Extensions of classical hydrodynamics. J. Stat. Phys. 132(3), 581–602 (2008)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Gurtin M.E.: Two-phase deformations of elastic solids. Arch. Rat. Mech. Anal. 84(1), 129 (1983)MathSciNetGoogle Scholar
  24. 24.
    Ivanova, E., Vilchevskaya, E.: Description of thermal and micro-structural processes in generalized continua: Zhilin’s method and its modifications. In: Altenbach, H., Forest, S., Krivtsov, A.M. (eds.) Generalized Continua as Models for Materials, pp. 179–197. Springer, Berlin, Heidelberg (2013)Google Scholar
  25. 25.
    Kikoin, J.K. (ed.): Tables of Physical Values. Handbook. Atomizdat, Moscow (1976)Google Scholar
  26. 26.
    Klippel A., Müller I.: Plant growth—a thermodynamicist’s view. Cont. Mech. Thermodyn. 9(3), 127–142 (1997)CrossRefzbMATHGoogle Scholar
  27. 27.
    Kondepudi D., Prigogine I.: Modern Thermodynamics. From Heat Engines to Dissipative Structures. Wiley, New York (1998)zbMATHGoogle Scholar
  28. 28.
    Kotake S.: Microscale Energy Transport, Chap. Molecular clusters, pp. 167–186. Taylor & Francis, London (1998)Google Scholar
  29. 29.
    Kwak H.Y., Kim Y.W.: Homogeneous nucleation and macroscopic growth of gas bubble in organic solutions. Int. J. Heat Mass Transf. 41, 757–767 (1998)CrossRefzbMATHGoogle Scholar
  30. 30.
    Kwak H.Y., Lee S.: Homogeneous bubble nucleation predicted by a molecular interaction model. ASME J. Heat Transf. 133, 714–721 (1991)CrossRefGoogle Scholar
  31. 31.
    Landau L., Lifshitz E.: The Classical Theory of Fields, vol. 2, 4th edn. Butterworth-Heinemann, London (1975)Google Scholar
  32. 32.
    Loicyanskii L.G.: Mekhanika Zhidkosti i Gaza (Mechanics of Fluids, in Russ.). Nauka, Moscow (1987)Google Scholar
  33. 33.
    Marx D.: Proton transfer 200 years after von grotthuss: insights from ab initio simulations. ChemPhysChem 7(9), 1848–1870 (2006)CrossRefGoogle Scholar
  34. 34.
    Müller I.: A History of Thermodynamics: The Doctrine of Energy and Entropy. Springer, Berlin (2007)Google Scholar
  35. 35.
    Müller I., Müller W.H.: Fundamentals of Thermodynamics and Applications: With Historical Annotations and Many Citations from Avogadro to Zermelo. Springer, Berlin (2009)Google Scholar
  36. 36.
    Müller I., Weiss W.: Entropy and Energy: A Universal Competition. Springer, Berlin (2005)Google Scholar
  37. 37.
    Peng X.: Micro Transport Phenomena During Boiling. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  38. 38.
    Peng X.F., Liu D., Lee D.J.: Cluster dynamics and fictitious boiling in microchannels. Int. J. Heat Mass Transf. 43, 4259–4265 (2000)CrossRefzbMATHGoogle Scholar
  39. 39.
    Pines, B.Y.: Odnofokusnye rentgenovskie trubki i prikladnoi rentgenovskii analiz (Monofocus X-ray Tube and Applied X-ray Analysis, in Russ.). Tekhniko-teoreticheskaya literatura, Moscow (1955)Google Scholar
  40. 40.
    Prigogine I.: Introduction to Thermodynamics of Irreversible Processes. Charles C. Thomas Publishers, Sprindfield (1955)Google Scholar
  41. 41.
    Prigogine I., Defay R.: Chemical Thermodynamics. Longmans, London (1988)Google Scholar
  42. 42.
    Prokhorov, A.M. (ed.): Physical Encyclopaedia, vol. 3: Magnetoplasma—Poynting Theorem. Bol’shaya Rossiiskaya Encyklopedia, Moscow (1992)Google Scholar
  43. 43.
    Spickermann, C.: Phase transitions. In: Entropies of Condensed Phases and Complex Systems, Springer Theses, pp. 177–210. Springer, Heidelberg (2011)Google Scholar
  44. 44.
    Truesdel C.: Rational Thermodynamics. Springer, New York (1984)CrossRefGoogle Scholar
  45. 45.
    Truesdell, C., Toupin, R.: The classical field theories. In: Flügge, S. (ed.) Encyclopedia of Phycics, vol. III/1. Springer, Heidelberg (1960)Google Scholar
  46. 46.
    van der Waals J.D.: Thermodynamische theorie der kapillaritSt unter voraussetzung stetiger dichteSnderung. Zeitschrift fnr Physikalische Chemie 13, 657–725 (1894)Google Scholar
  47. 47.
    Wagner W., Pruss A.: The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. J. Phys. Chem. Ref. Data 31(2), 387–535 (2002)ADSGoogle Scholar
  48. 48.
    Wilmanski K.: Thermomechanics of Continua. Springer, Heidelberg (1998)CrossRefzbMATHGoogle Scholar
  49. 49.
    Zeng J.B., Li L.J., Liao Q., Cui W.Z., Chen Q.H., Pan L.M.: Simulation of phase transition process using lattice boltzmann method. Chin. Sci. Bull. 54(24), 4596–4603 (2009)CrossRefGoogle Scholar
  50. 50.
    Zhilin P.A.: Racional’naya mekhanika sploshnykh sred (Rational Continuum Mecanics, in Russ.). Politechnic University Publishing House, St. Petersburg (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Elena N. Vilchevskaya
    • 1
    • 2
  • Elena A. Ivanova
    • 1
    • 2
  • Holm Altenbach
    • 3
  1. 1.Institute for Problems in Mechanical Engineering of the Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Department of Theoretical MechanicsSt. Petersburg State Polytechnical University (SPbSPU)St. PetersburgRussia
  3. 3.Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für MaschinenbauOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

Personalised recommendations